A charge of magnitude 1.6 × 10 - 19 C is moving in a circle of radius 5 cm in a uniform magnetic field 0.5 T . After applying E = 0.15 V m - 1 charge starts moving in a straight line mass of charge wi

Question

A charge of magnitude 1.6 × 10 - 19 C is moving in a circle of radius 5 cm in a uniform magnetic field 0.5 T . After applying E = 0.15 V m - 1 charge starts moving in a straight line mass of charge will be

TestHub · Accepted Answer

For a particle to move in a circle under magnetic field

$q V B = \frac{m v^{2}}{R}$ ...(i)

For a particle to move in a straight line

In both magnetic field and electric field

$q V B = 2 E$

$\Rightarrow V = \frac{E}{B}$ ...(ii)

From (i) to (ii)

$q B = \frac{m v}{R}$

$= \frac{m . E}{B R}$

$\Rightarrow m = \frac{q E^{2} R}{E} = \frac{1.6 \times 10^{- 13} \times {0.5}^{2} \times 10^{- 2}}{0.15} kg = \frac{4}{3} \times 10^{- 20} kg$

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